Las argumentaciones matemáticas desde la visión de la socioepistemología

The objective proposed in this investigation is to understand the sociocultural
character of mathematical argumentations.

The raised hypothesis affirm that mathematical argumentations are constructions
that reflect characteristics of sociocultural scenes, and that argumentation forms
are also constructed outside academic scenes and these are not based on the
aristotelian logic and they arrive to mathematical classroom, not agreeing their
characteristics to the argumentations which are often waited in academic scenes.

In the case of the argumentations strongly based on principles of the aristotelian
logic, they are characteristic from logical thought of cultures with influence of the
classic logic and they are not present in other scenes without that influence. We
can affirm that they are not innate and therefore not inherent of human reasoning,
but that depend on the scene in which the individual acts.

On the other hand, we may detect the presence of different types of
argumentations in mathematical classroom that sometimes cannot be explained
from the aristotelian logic. The absence of argumentations based on the
aristotelian logic at nonmathematical scenes, also allows us to understand that in
that sociocultural product character.

This investigation is oriented to study the processes of social construction of the
mathematical knowledge, fixing the attention to its fundamentation. Basically this
investigation was carried out from the analysis of sources referred to the logical
thought in different sociocultural scenes, in order to identify the forms of
argumentation used, and experimentations with students through analysis of its
productions in the classroom and interviews and questionnaires.